Season the salmon liberally on both sides with salt and pepper and let sit in the refrigerator for between 30 minutes and 4 hours, or soak it in brine in the refrigerator for 1 to 2 hours, depending on its thickness. Place a plate on top of the salmon to keep it submerged. In either case, pat the salmon dry just before sautéing. If you've used brine, season it only with pepper.

Heat the oil or butter in heavy-bottomed (preferably nonstick) sauté pan just large enough to hold the salmon, until the oil forms ripples and barely begins to smoke.
If you're sautéing skin-on fillet, place them in the pan skin side down and press on them firmly for the first 2 minutes with the back of a spatula to keep the fillet from curling.

If you're sautéing skin-off fillets, put the most attractive side down -the side that was facing the inside of the salmon, not the side that once had the skin attached- in the pan first (so that it will be facing up when you turn the fillets over). For inch-thick fillets or steaks, sauté over high heat for 3 to 5 minutes on the first side, turn then over with a spatula and sauté for 2 to 3 minutes on the second side.

If the salmon starts to brown or the oil or butter smokes, turn the heat down to medium. Keep in mind that the total cooking time should be 8 to 10 minutes per inch of total thickness (depending on how you like your salmon done) and that the salmon should spend more time sautéing on the first side (the eventual presentation side) so that you're sure to end up with a savory golden crust or crisp skin. Adjust the cooking times according to the salmon's thickness.

Remove the salmon from the pan with a spatula and pat it dry on both sides with a paper towel to get rid of any taste of burned fat. Serve immediately on hot plates.

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